U.S. patent application number 13/649587 was filed with the patent office on 2013-08-22 for systems for real-time available transfer capability determination of large scale power systems.
This patent application is currently assigned to Bigwood Technology, Inc.. The applicant listed for this patent is Bigwood Technology, Inc., School of Electrical Engineering and Automation, Tianjin University, Tokyo Electric Power Company, Inc.. Invention is credited to Hsiao-Dong Chiang, Yasuyuki Tada, Cheng-Shan Wang.
Application Number | 20130218494 13/649587 |
Document ID | / |
Family ID | 48982918 |
Filed Date | 2013-08-22 |
United States Patent
Application |
20130218494 |
Kind Code |
A1 |
Chiang; Hsiao-Dong ; et
al. |
August 22, 2013 |
Systems for Real-Time Available Transfer Capability Determination
of Large Scale Power Systems
Abstract
A system for accurately determining real-time Available Transfer
Capability and the required ancillary service of large-scale
interconnected power systems in an open-access transmission
environment, subject to static and dynamic security constraints of
a list of credible contingencies, including line thermal limits,
bus voltage limits, voltage stability (steady-state stability)
constraints, and transient stability constraints.
Inventors: |
Chiang; Hsiao-Dong; (Ithaca,
NY) ; Tada; Yasuyuki; (Tokyo, JP) ; Wang;
Cheng-Shan; (Tianjin, CN) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Bigwood Technology, Inc.;
Tokyo Electric Power Company, Inc.;
Tianjin University; School of Electrical Engineering and
Automation, |
|
|
US
US
US |
|
|
Assignee: |
Bigwood Technology, Inc.
Ithaca
NY
School of Electrical Engineering and Automation, Tianjin
University
Tianjin
Tokyo Electric Power Company, Inc.
Tokyo
|
Family ID: |
48982918 |
Appl. No.: |
13/649587 |
Filed: |
October 11, 2012 |
Related U.S. Patent Documents
|
|
|
|
|
|
Application
Number |
Filing Date |
Patent Number |
|
|
61545682 |
Oct 11, 2011 |
|
|
|
Current U.S.
Class: |
702/61 |
Current CPC
Class: |
Y02E 60/00 20130101;
H02J 3/001 20200101; H02J 3/06 20130101; Y04S 20/222 20130101; H02J
2203/20 20200101; Y02B 70/3225 20130101; G01R 21/006 20130101; H02J
3/24 20130101; Y04S 40/20 20130101 |
Class at
Publication: |
702/61 |
International
Class: |
G01R 21/00 20060101
G01R021/00 |
Claims
1. A method of evaluating a static power transfer capability (PTC)
of an interconnected power system with respect to a power transfer
transaction subject to security constraints comprising the steps
of: a) initializing the evaluation by building a power transfer
vector to represent the proposed power transfer transaction and
forming parameterized power flow equations by incorporating the
power transfer vector into base-case power flow equations; b)
ranking a plurality of contingencies with respect to static
security violation criteria to determine any associated violated
constraints; c) computing a first-contingency PTC, and identifying
at least one corresponding binding contingency; d) ranking a
plurality of contingency-constrained PTCs and first contingency
incremental transfer capabilities (FCITCs) giving a PTC for the
interconnected power system with respect to a power transfer
transaction; and e) outputting the PTC and an FCITC for the power
system with the power transaction under each binding contingency
and the associated violated constraints.
2. The method of claim 1, in which the initializing step (a)
comprises the steps of: (i) building a the power transfer vector b
to mathematically represent the power transfer transaction; (ii)
forming parameterized power flow equations by incorporating the
power transfer vector b into base-case power flow equations
f(x)-.lamda.b=0; and (iii) initializing a generation/load condition
number .lamda. by setting .lamda.=.lamda..sub.0 to the base
case.
3. The method of claim 2, in which the ranking step (b) comprises
the steps of: (i) using a look-ahead scheme to rank the set of
contingencies L in terms of branch MVA violation into a ranked set
of contingencies L(mva); (ii) using a look-ahead scheme to rank the
set of contingencies L in terms of bus voltage violation into a
ranked set of contingencies L(volt); and (iii) using a look-ahead
scheme to rank the set of contingencies L in terms of load margin
into a ranked set of contingencies L(margin).
4. The method of claim 3, in which the computing step (c) comprises
the steps of: (i) selecting the top N.sub.a contingencies from the
ordered set L(mva), the top N.sub.b contingencies from the ordered
set L(volt), and the top N.sub.c contingencies from the ordered set
L(margin); (ii) renumbering the contingencies from step (c)(i) into
l.sub.1, l.sub.2 . . . , l.sub.N.sub.a.sub.+N.sub.b.sub.+N.sub.c;
(iii) if there are any sets of duplicate contingencies, eliminating
all but one contingency from each set of duplicate contingencies;
(iv) defining a new set L.sub.static .tangle-solidup.{I.sub.0,
I.sub.1, . . . , I.sub.N.sub.total}, where I.sub.0 represents the
base case power system; (v) for each contingency in L.sub.static,
perform the following steps: (A) setting j=0 (B) using CPFLOW to
compute solutions of parameterized power flow equations under
contingency l.sub.i for each generation/load condition number
.lamda..sub.j=.lamda..sub.j+.DELTA..lamda..sub.j, where
.DELTA..lamda..sub.j=0 if j=0; otherwise .DELTA..lamda..sub.j is
determined by the step-size control in CPFLOW; (C) if the
post-contingency power flow solution [X(.sub.v,.lamda.].sub.l)
satisfies the following static security constraints voltage:
V.sup.m.ltoreq.V(l.sub.v.lamda..sub.j).ltoreq.V.sup.M line current:
I.sup.m.ltoreq.I(l.sub.v.lamda..sub.j).ltoreq.I.sup.M facility
loading: g(l.sub.v.lamda..sub.j).ltoreq.0 then set j=j+1 and repeat
from step (v)(B); otherwise, set Cbind=the corresponding violated
constraints and continue to step (v)(D); (D) if
|.lamda..sub.j-.lamda..sub.j-1|<, continue from step (v)(E),
otherwise, set ? = ? 2 ? indicates text missing or illegible when
filed ##EQU00008## and use CPFLOW to compute the solutions of the
parameterized power flow equations under contingency l.sub.i for
the generation/load condition number .lamda..sub.i= .lamda..sub.j;
(I) if the post-contingency power flow solution X(l.sub.g
.lamda..sub.j) satisfies the static security constraints, then set
.lamda..sub.j-1= .lamda..sub.j and repeat this step (v)(D);
otherwise set .lamda..sub.j= .lamda..sub.j, and Cbind=the
corresponding violated constraints and repeat this step (v)(D); (E)
recording the contingency I.sub.j, the generation/load condition
number .lamda..sub.j=.lamda..sub.j-1, and the corresponding
violated constraints CV.sub.j, giving the first-contingency
available transfer capability under contingency l.sub.j as
.lamda..sub.j .lamda..sub.0 with the binding constraint CV.sub.j;
(F) if t<N.sub.total, set i=i+1 and go to step (v)(1);
otherwise, go to step (d).
5. The method of claim 4, in which the step (d) of ranking
comprises the steps of: (i) ranking the set L.sub.static according
to each value .lamda..sub.j obtained in step (c)(v)(E), such that:
the ranked contingency set is L.sub.static={l.sub.1, l.sub.2, . . .
l.sub.total} such that .lamda..sub.1.gtoreq. .lamda..sub.2.gtoreq.
. . . .gtoreq. .lamda..sub.total, the first-contingency PTC or
FCITC subject to static voltage stability constraints and static
security constraints of the contingency set L is
.lamda..sub.total=( .lamda..sub.total-.lamda..sub.0), the binding
contingency l.sub.total; the associated violated constraint is
CV.sub.total; and the PTC under contingency I.sub.j, is
.lamda..sub.j=( .lamda..sub.j-.lamda..sub.0) with the binding
constraint CV.sub.j, for j=1, 2, . . . ,
total-1.sub..quadrature..
6. The method of claim 1, in which in step (e), PTC is expressed in
terms of amount of PTC between sending areas and receiving
areas.
7. The method of claim 1, in which in step (e), PTC is represented
in terms of base-case interface power flows of a transmission
interface.
8. The method of claim 1, in which in step (e), PTC is displayed as
a two-dimensional nomogram in terms of two interface flows.
9. The method of claim 8, in which the nomogram is created by the
steps of: (a) separating source generators into two groups G.sub.1
and G.sub.2, and assign a.sub.1=0 and a.sub.2=1; (b) computing
b.sub.g=a.sub.1b.sub.g1+a.sub.2b.sub.g2; (c) computing a
one-dimensional system-wide static PTC and corresponding interface
static PTC's along the direction b.sub.g; (d) assigning different
values for a and a 7 in the equation of step (b) and repeat the
method from step (b) to compute all points on the nomogram curve;
(e) exporting the static PTC nomogram curve and the corresponding
limiting contingency of each computed point on the nomogram
boundary.
10. The method of claim 1, further comprising the step of computing
a difference between the PTC and a current actual power flow,
giving a real-time available transfer capacity (ATC).
11. An energy-margin-based search method to select a next operating
point between two known operating points on a P-V curve, comprising
the steps of: (a) using a BCU method to compute an energy margin of
contingency i at a base-case .lamda.=.lamda..sub.0, such that the
energy margin of contingency i is W.sub.i.sup.(.lamda..sup.0.sup.);
(b) if W.sub.i.sup.(.lamda..sup.0.sup.)>0, designating
contingency i as stable; (c) using the BCU method to compute the
energy margin of contingency i at another loading condition,
.lamda.=.lamda..sub.i, such that the energy margin of contingency i
is W.sub.i.sup.(.lamda..sup.1.sup.); (d) if
W.sub.i.sup.(.lamda..sup.1.sup.)<0, designating contingency i as
unstable at the loading condition .lamda.=.lamda..sub.1, such that
the power transfer limit (PTL) relative to contingency i lies
between the two loading conditions .lamda..sub.0.lamda..sub.1; (e)
using a one-dimensional search method, identify the PTL subject to
contingency i; (f) computing a new loading condition .lamda. 2 =
.lamda. 0 + .lamda. 1 2 ; ##EQU00009## (g) computing the energy
margin at the new loading condition W.sub.i(.lamda..sub.2); (h)
computing the next loading level ? = ? + ? ? - W .quadrature. (
.lamda. 0 ) W .quadrature. ( .lamda. 1 ) ; ? indicates text missing
or illegible when filed ##EQU00010## and (i) repeating the method
for the next loading condition to be evaluated for transfer
stability assessment .lamda..sub..quadrature.=.lamda..
12. The method of claim 11, wherein the one-dimensional search
method of step (e) is a bracketing algorithm, a bisection
algorithm, a secant algorithm or Ridder's algorithm.
13. A method of evaluating a dynamic power transfer capability
(PTC) of an interconnected power system comprising the steps of:
(a) applying the CPFLOW method to compute a P-V curve for a
base-case power system for a proposed power transaction; (b)
applying the TEPCO-BCU method to the base-case operating point to
perform transient stability analysis of the operating point subject
to a contingency list; (c) if there is an insecure or critical
contingency at the current base-case operating point, then stop the
method; (d) setting the base-case operating point as the lower
bound of the dynamic PTC and record the corresponding critical
contingencies and their corresponding energy margin; (e) applying
the TEPCO-BCU method to a base-case nose point to perform a
transient stability analysis subject to the entire contingency
list; (f) if there is no insecure or critical contingency at the
base-case nose point, then output the dynamic PTC as the same value
of static PTC and stop; (g) setting the base-case nose point as the
upper bound of the dynamic PTC; (h) recording the corresponding
insecure and critical contingencies and their corresponding energy
margin; (i) selecting a loading condition on the P-V curve between
a lower bound and an upper bound of the dynamic PTCs based on an
energy-margin one-dimensional search method; (j) applying the
TEPCO-BCU method to the selected loading condition from step (i) to
perform transient stability analysis subject to the newly-updated
contingency list; (k) if at least one insecure contingency is
detected, set the current loading condition as the upper bound of
the dynamic PTC; otherwise, update the lower bound of dynamic PTC
by the currently selected loading condition; and (l) if a
difference between the lower bound and upper bound of the dynamic
PTC is larger than a selected number, then repeat the method from
step (i): (m) exporting the top-limiting contingencies and compute
the corresponding dynamic PTCs.
14. The method of claim 13, wherein the one-dimensional search
method of step (i) is a bracketing algorithm, a bisection
algorithm, a secant algorithm or Ridder's algorithm.
15. The method of claim 13, wherein the one-dimensional search
method of step (i) is a golden bisection algorithm.
16. A method of creating a dynamic PTC nomogram graph in terms of
two interface flows, in which a first interface path is associated
with the X axis and a second interface path is associated with the
Y axis, a group of source generators responsible for a flow change
in the X axis path is denoted as G.sub.1, and a group of source
generators responsible for a power flow change in the Y axis path
is denoted as G.sub.2, the method comprising the steps of: (a)
assigning a.sub.1=0 and a.sub.2=1; (b) computing b.sub.g using the
equation b.sub.g=a.sub.1b.sub.g1+a.sub.2b.sub.g2; (c) computing the
one-dimensional system-wide dynamic PTC and the corresponding
interface dynamic PTC's along the directions b.sub.g; (d) assigning
different values for a.sub.1 and a.sub.2 in the equation of step
(b), and repeat from step (b) to compute all points on the nomogram
curve: and (e) exporting the dynamic PTC nomogram curve and the
corresponding limiting contingency of each computed point on the
nomogram boundary.
17. A method of computing a power transmission capability (PTC)
subject to static and dynamic security constraints, comprising the
steps of: (a) applying the CPFLOW method to compute the P-V curves
for the base-case power system for a proposed power transaction;
(b) computing the static PTC subject to static constraints of a
credible contingency list; (c) determining a corresponding
operating point termed as the base-case static-security-constrained
(SSC) operating limit point; (d) recording a corresponding limiting
contingency for the SSC; (e) applying the TEPCO-BCU method to a
current base-case operating point, obtained from a state
estimation, to perform transient stability analysis of the
operating point subject to a contingency list; (f) if there is an
insecure or critical contingency at the current base-case operating
point, output the real-time static and dynamic PTC as zero and stop
the method; (g) setting the base-case operating point as the lower
bound of the dynamic PTC and record the corresponding critical
contingencies and their corresponding energy margin; (h) applying
the TEPCO-BCU method to the base-case static-security-constrained
(SSC) operating limit point to perform transient stability analysis
subject to the contingency list; (i) if there is no insecure or
critical contingency at the base-case SSC operating limit point,
then continue the method at exporting step (p); (j) setting the
base-case SSC operating limit point as the upper bound of the
dynamic PTC; (k) recording the corresponding insecure and critical
contingencies and their corresponding energy margin; (l) selecting
a loading condition on the P-V curve between the lower bound and
the upper bound of the dynamic PTCs based on an energy-margin
one-dimensional search method; (m) applying the TEPCO-BCU method to
the selected loading condition of step (k) to perform transient
stability analysis subject to the newly-updated contingency list;
(n) if at least one insecure contingency is detected, set the
current loading condition as the upper bound of the dynamic PTC;
otherwise, update the lower bound of dynamic PTC by the currently
selected loading condition; (o) if a difference between the lower
bound and upper bound of the dynamic PTC is larger than a specified
number, then continue the method at step (i); (p) exporting the
top-limiting contingencies and the corresponding static and dynamic
PTCs.
18. The method of claim 17, wherein the one-dimensional search
method of step (l) is a bracketing algorithm, a bisection
algorithm, a secant algorithm or Ridder's algorithm.
19. The method of claim 17, wherein the one-dimensional search
method of step (l) is a golden bisection algorithm.
20. The method of claim 17, further comprising the step of
computing a difference between the PTC and a current actual power
flow, giving a real-time static and dynamic available transfer
capacity (ATC).
Description
REFERENCE TO RELATED APPLICATIONS
[0001] This application claims one or more inventions which were
disclosed in Provisional Application No. 61/545,682, filed Oct. 11,
2011, entitled "Systems for Real-Time Available Transfer Capability
Determination of Large Scale Power Systems". The benefit under 35
USC .sctn.119(e) of the United States provisional application is
hereby claimed, and the aforementioned application is hereby
incorporated herein by reference.
BACKGROUND OF THE INVENTION
[0002] 1. Field of the Invention
[0003] The invention pertains to the field of electric power
distribution. More particularly, the invention pertains to analysis
of large-scale interconnected power systems.
[0004] 2. Description of Related Art
[0005] The Federal Energy Regulatory Commission's (FERC)
open-access NOPR has created far-reaching changes in the wholesale
electric industry in the United States. To enforce the open-access
transmission policy, FERC further defined a term "Available
Transfer Capacity" (ATC) to inform all energy market participants
regarding the maximum power transfer capability of a system. Hence,
the development of a real-time method for accurately determine
available transfer capability is essential in power systems within
the open access environment. One main challenge is to quickly and
accurately compute the real-time available transfer capability
under varying loading conditions, taking into account the static as
well as dynamic security constraints of a large number of
contingencies.
[0006] The de-regulated electricity market has resulted in rather
rapid changes in operating conditions. System operators now face
more new, unknown power flow patterns than ever before. At the same
time, economic pressure on the electricity market and on grid
operators, coupled with limited investment in new generation and
transmission networks, push power systems close to their stability
limits. The uncertainty and variability brought about by renewable
energies may further push power systems ever close to or beyond
their stability limits.
[0007] Available Transfer Capability (ATC) has been used to guide
power system operations for setting transfer limits on transmission
corridors and key tie-lines. Currently, ATC is mostly calculated
using off-line, worst-case scenarios and it results in very
conservative calculations of power transfer limits. This
traditional tool of off-line ATC calculation is inadequate. Hence,
there is a need to calculate the ATC based on actual operating
conditions.
[0008] Power transfer capability (PTC) refers to the capacity and
ability of a transmission network to allow for the reliable
transfer of electric power from an area of supply to an area of
need by way of all transmission lines (or paths) between two areas
under assumed system conditions. In this invention, the
terminologies of power transfer capability (PTC) and the power
transfer limit (PTL), i.e. (PTC under a specified control scheme)
will be used interchangeably. The assumed (current and near-term)
operating conditions include several projected factors such as the
expected load demands, near-term real power dispatch, the system
configuration, and the scheduled power transfers among the
interconnected systems.
[0009] The power transfer capabilities proposed by NERC are
generally the first contingency incremental transfer capability
(FCITC) or first contingency total transfer capability (FCTTC) for
predicted peak load conditions. FCITC is the amount of electric
power incremental above a normal base power that can be transferred
in a reliable manner based on all of the following conditions:
[0010] (1) for the existing or planned system configuration, and
with normal (pre-contingency) operating procedures in effect, all
facility loadings are within normal ratings and all voltages are
within normal limits, [0011] (2) the electric system is capable of
absorbing the dynamic power swings, and remaining stable following
a disturbance that results in the loss of any single electric
system element, such as a transmission line, transformer, or
generation unit, [0012] (3) after the dynamic power swings subside
following a disturbance that results in the loss of any single
electric system element as described in (2) above, and after the
operation of any automatic operating systems, but before any
post-contingency operator-initiated system adjustments are
implemented, all transmission facility loadings are within
emergency ratings and all voltages are within emergency limits.
[0013] Note that condition (1) is related to the static security
constraints under the first contingency of the pre-contingency
operating conditions while condition (3) is concerned with the
static security constraints of the post-contingency operating
conditions. Condition (2) is the typical (angle) transient
stability constraint and may not include the voltage dip problem
during transients as constraints.
[0014] A set of interface tie-lines can be defined between a
sending area and a receiving area. FIG. 1 illustrates the concept
of interface tie-lines.
[0015] In FIG. 1 the transmission lines L11, L12, . . . , L1r
between the sending area and the receiving area form a set of
interface tie-lines. The line (real) power flows, p11, p12, . . . ,
p1r in the set of interface tie-lines form the interface tie-line
flow.
[0016] The system-wide PTC can be mapped into an interface tie-line
PTC. Depending on the selection of interface tie-lines, the
corresponding interface tie-line PTC will be different. FIG. 2
illustrates the interface tie-line dependent PTC. The system-wide
PTC can be hard to visualize while the interface dependent PTCs are
amenable to visualization.
[0017] The Continuation Power Flow Method (or "CPFLOW") is a method
for tracing power system behavior described in a paper "CPFLOW:
Tool for Tracing Power System Steady-State Stationary Behavior Due
to Load and Generation Variations", Chiang, Sha and Balu, IEEE
Transactions on Power Systems, Vol. 10, No. 2, pages 623-634, May
1995, which is incorporated herein by reference.
[0018] A BCU method is a systematic method to find the controlling
unstable equilibrium point, as disclosed in U.S. Pat. No. 5,483,462
"On-line method for determining power system transient stability"
granted to Dr. Hsiao-Dong Chiang, one of the inventors herein,
which is incorporated herein by reference.
[0019] A BCU Classifier is a method for ensuring that unstable
contingencies are captured and reduced, as described in
"Development of BCU Classifiers for On-Line Dynamic Contingency
Screening of Electric Power Systems", Chiang, Wang and Li, IEEE
Transactions on Power Systems, Vol. 14, No. 2, pages 660-666, May
1999.
SUMMARY OF THE INVENTION
[0020] The invention describes a system for accurately determining
real-time Available Transfer Capability (ATC) and the required
ancillary service of large-scale interconnected power systems in an
open-access transmission environment, subject to static and dynamic
security constraints of a list of credible contingencies, including
line thermal limits, bus voltage limits, voltage stability
(steady-state stability) constraints, and transient stability
constraints.
BRIEF DESCRIPTION OF THE DRAWING
[0021] FIG. 1 shows a diagram of interface tie-lines.
[0022] FIG. 2 shows a diagram of an interface tie-line dependent
Power Transfer Capability (PTC), mapped from a system-wide PTC
[0023] FIG. 3 shows a block diagram of schemes for ranking a list
of contingencies in terms of load margin, voltage limit and thermal
limit.
[0024] FIG. 4 shows a graph of how a stress pattern spans the
entire feasible generation/load stress space
[0025] FIG. 5 shows diagrams of how a system-wide static PTC
nomogram is mapped into each pair of tie-line interfaces static PTC
nomogram.
[0026] FIG. 6 shows a diagram of a tie-line power flow measured by
PMU's placed across the interface while the static PTC is
computed.
[0027] FIG. 7 shows a diagram of tie-line power flow of interface
#i as measured by PMU's placed across interface #i, while the
tie-line power flow of interface #j is measured by PMU's placed
across interface #j.
[0028] FIG. 8 shows a block diagram of an architecture of a
PMU-assisted real-time static available transfer capability
determination system.
[0029] FIG. 9 shows an architecture of a PMU-assisted,
load-margin-based, real-time static available transfer capability
determination system.
[0030] FIG. 10 shows a graphic of base-case interchange power flows
in a subsystem composed of 9 areas with 1135 buses and 2216
transmission lines.
[0031] FIG. 11 shows a tale of accuracy of a BCU-limiter, as
compared with the time-domain approach on 12 contingencies in terms
of error.
[0032] FIG. 12 shows a diagram of tie-line power flow of an
interface measured by PMU's placed across the interface while the
dynamic PTC is computed by the method of the invention.
[0033] FIG. 13 shows a block diagram of an architecture of a
PMU-assisted, real-time dynamic available transfer capability
determination system with output displays of one-dimensional meters
for each interface.
[0034] FIG. 14 shows a block diagram of an architecture of a
PMU-assisted, real-time dynamic available transfer capability
determination system with output displays via two-dimensional
nomograms for each pair interfaces.
[0035] FIG. 15 shows a diagram of tie-line power flow in an
interface measured by PMU's placed across the interface while the
static and dynamic PTC is computed by the method of the
invention.
[0036] FIG. 16 shows a graph of the output of a PMU-assisted,
real-time static and dynamic ATC determination system, expressed as
a two-dimensional nomogram.
[0037] FIG. 17 shows a block diagram of an architecture of a
PMU-assisted, real-time static and dynamic available transfer
capability determination system with one-dimensional meter displays
for each interface.
[0038] FIG. 18 shows a block diagram of an architecture of a
PMU-assisted, real-time static and dynamic available transfer
capability determination system with two-dimensional monogram
displays for each pair interfaces.
DETAILED DESCRIPTION OF THE INVENTION
[0039] The Real-Time ATC system developed in this invention is
designed to provide power system operators with critical
information including the following: [0040] (i) Assessment of
real-time ATC of a power system subject to both static and
transient stability constraints of a list of contingencies. [0041]
(ii) Available power transfer capability and power transfer limits
at key interfaces subject to both static and transient stability
constraints of a list of contingencies. [0042] (iii) The limiting
contingencies and binding constraints for power transfer
limits.
[0043] The outputs of the real-time ATC system include the
following: [0044] Overall status of the system; i.e. system-wide
ATC, and the corresponding binding constraints (line thermal
limits, or bus voltage limits, or voltage stability (steady-state
stability) constraints or transient stability constraints) and the
limiting contingency. [0045] power transfer limits at key
interfaces, the corresponding limiting contingencies (contingency
details such as fault type, fault location, and circuits lost) and
the corresponding binding constraints. [0046] available power
transfer capability and the corresponding limiting contingencies
(contingency details such as fault type, fault location, and
circuits lost). The distinguished features of the real-time method
include the following Functional Viewpoint: [0047] 1. It computes
ATC and FCITC, and identifies the corresponding (the most severe)
contingency, and the associated binding constraints. [0048] 2. It
identifies and ranks the top severe contingencies in terms of their
impacts on ATC and FCITC. [0049] 3. For each ranked contingency, it
computes ATC and FCITC of the power system subject to the
contingency and the associated binding constraint. [0050] 4. It
identifies the bottlenecks of ATC in terms of locations of
bottlenecks, types of binding constraint and the associated binding
contingency. [0051] 5. It handles all the static security
constraints of a given contingency list. [0052] 6. It facilitates
the incorporations of the dynamic security constraints. [0053] 7.
It determines the required ancillary services.
Probabilistic Analysis:
[0053] [0054] 8. It allows a probabilistic treatment of each
contingency to compute ATC and FCITC.
Model Viewpoint:
[0054] [0055] 9. It is based on a full power system nonlinear
modeling [0056] 10. It takes into account the effects of control
devices [0057] 11. It models the general characteristic of power
system operating environments
Control Viewpoint
[0057] [0058] 12. It offers a highly effective environment for the
development of control schemes to increase ATC and FCITC. [0059]
13. It provides a platform to take proactive action in computing
ATC and FCITC and to prepare remedy control.
[0060] PTC of an interconnected power system depends heavily on
underlying power transactions. In fact, the PTC and its associated
binding constraints of an interconnected power system can be very
different for different proposed power transactions. Hence, it is
important to specify the proposed power transaction in calculating
the PTC with respect to the power transaction.
[0061] Given a set of proposed power transactions, the objective of
a transfer capability computation is to determine the maximum
transfer value for a proposed power transaction or simultaneous
power transactions. The problem formulation upon which the
calculation is based must have the following general
characteristics: [0062] (C1) it represents a realistic operating
condition or expected future operating condition. To achieve (C1),
the activation of the following control devices normally expected
in any operating procedures should be included in the simulations:
(i) Switchable shunts and static VAR compensators, (ii) ULTC
Transformers, (iii) ULTC phase shifter, (iv) Static tap changer and
phase shifter, (v) DC Network. In order to completely describe the
actual power flow in the entire interconnected systems network and,
in particular, the unintended electric power flows on these
neighboring or adjacent systems known as parallel path flows, a
detailed nonlinear power flow analysis of the interconnected system
must be performed. [0063] (C2) it conforms with the requirements of
the transfer capability definitions by NERC. To achieve (C2), it is
important to accurately represent the proposed power transaction.
[0064] (C3) it considers single contingency facility outages that
result in conditions most restrictive to electric power transfers.
To achieve (C3), the static and dynamic security assessments of the
first contingency from a contingency list on an interconnected
power system is required.
[0065] The basic information required for the system-wide PTC
evaluations includes the following: [0066] (1) the current
operating condition (obtained from the state estimator and the
topological analyzer); [0067] (2) a base case power system model
with control devices, reactive power generation limits; [0068] (3)
load forecast for the next period (say, next 15 minutes) of each
bus; [0069] (4) a set of proposed power transactions, such as (i) a
point-to-point MW transaction, or (ii) a slice-of-the-system sale,
or (iii) a network service, for the next period; [0070] (5)
generation scheduling (or generation participation factor) to
accommodate load increases or/and to accommodate power
transactions; and [0071] (6) a list of credible contingencies.
[0072] In addition to the above basic information, the information
of how to model the control actions during the process of step
increases in loads and generations is required. These control
actions include the static VAR compensator, TCSC, tap changer,
synchronous condenser voltage/Mvar, LTC transformer voltage
control, phase-shiftier controls, and capacitor/reactor voltage
control, etc. . . . .
[0073] We present a method to represent a power transaction or a
set of power transactions. We also discuss the notion of
generation/load margin to a static security limit.
[0074] Given a load demand vector (i.e. real and reactive load
demands at each load bus) and a real generation vector (i.e. real
power generation at each generator bus), one can compute the state
of the power system (the complex voltage at each bus) by solving
the set of power flow equations.
[0075] Let P=P-Pand Q=Q-Q. The lowercase g represents generation
and the lowercase d represents load demand. The set of power flow
equations can be represented in compact form as
f ( x ) = [ P ( x ) - P Q ( x ) - Q ] = 0 , where x = ( v , .theta.
) ( 1 ) ##EQU00001##
[0076] Now one can investigate the steady-state behavior of the
power system under slowly varying loading conditions and real power
redispatch. For example, if one needs to trace the power system
state from the base-case generation/load condition [P.sub.d,
Q.sub.d, P.sub.g] to a new generation/load condition
[P.sub.d.sup.1, Q.sub.d.sup.1, P.sub.g.sup.1], then one can
parameterize the set of power flow equations as such
F(x,.lamda.)=f(x)-.lamda.b=0 (2)
where the generation/load vector b is
b .ident. [ P 1 - P 0 Q 1 - Q 0 ] ( 3 ) ##EQU00002##
[0077] It follows that the parameterized power flow equations
become the base-case power flow equations when .lamda.=0,
F ( x , 0 ) = [ P ( x ) - P 0 Q ( x ) - Q 0 ] = 0 ( 4 )
##EQU00003##
[0078] And when .lamda.=1, the power system is at the new
generation/load condition [P.sub.d.sup.1, Q.sub.d.sup.1,
P.sub.g.sup.1] and can be described by
F ( x , 1 ) = f ( x ) - b = [ P ( x ) - P 1 Q ( x ) - Q 1 ] = 0 ( 5
) ##EQU00004##
[0079] As shown in the above procedure, one can investigate the
effects of varying real power generations as well as varying load
demands on power system steady-state behaviors. In fact, one can
parameterize any change in PQ loads in conjunction with any change
in P generations by selecting an appropriate vector b.
[0080] Applying the above general setting to the problem of
computing PTC of interconnected power systems, the vector b can be
used to represent one or several of the following power
transactions and transmission service: [0081] Point-to-point MW
transaction--the real power at one load bus of the receiving area
varies while the others remain fixed and the real power at one
generator bus of the sending area varies while the others remain
fixed, [0082] Slice-of-the-system sale--both the real and reactive
power demand at a load bus of the receiving area vary and the real
power generation at some collection of generators of the sending
bus varies while the others are fixed, [0083] Network service--the
real and/or reactive power demands at some collection of load buses
of the receiving area vary and the real power generation at some
collection of generators of the sending bus varies while the others
are fixed, [0084] Reactive ancillary service--the reactive power
demands at a specific or some collection of load buses of the
receiving area vary and are balanced by the reactive generation
within the same area or at other surrounding areas.
[0085] We shall call the vector b the proposed power transaction
vector, and the scalar .lamda., the generation/load condition
number. The proposed power transaction vector b can be used to
represent a transaction involving simultaneous power transfers by
summing each power transaction vector, i.e. b=.SIGMA.b.sub.i, i=1,
2, . . . where the vector represents the ith power transaction.
[0086] The introduction of the power transaction vector and the
load generation condition number enable one to rigorously evaluate
available transfer capability of an interconnected system
satisfying the general characteristics (C1), (C2) and (C3) stated
above. For instance, one can compute the maximum value of the
generation/load condition number so that the resultant
interconnected power system satisfies all the constraints, which
are required in the general characteristics (C2) and (C3).
[0087] Due to the nonlinear nature of interconnected electric
systems, power transfer capabilities between two areas and their
associated binding constraints depend on a set of system
conditions. The power transfer capabilities and their associated
binding constraints can be significantly different for any other
set of system conditions, such as a different set of system load
demands, a different network configuration, a different power
transaction, or a different generation dispatch pattern. Hence,
transfer capability computations must be sufficient in system
modeling and scope to ensure that all equipment as well as system
limits of the entire interconnected systems network are properly
taken into account.
[0088] In general, power transfers cannot be forced through
pre-determined transmission paths, unless the paths are physically
controlled by control devices such as phase-shifters. Therefore,
power transfers will be distributed among all parallel paths
according to the laws of physics. As a result, simple bi-lateral
contracts between neighboring areas may not be sufficient to
describe the actual power flow. Detailed nonlinear power system
models must be used for analysis.
[0089] In addition, given a set of proposed power transactions, the
binding constraint which limits the system's PTC can be the
physical operating limits of an equipment/facility, or the bus
voltage constraint in the entire system including the sending, the
receiving as well as all neighboring areas, or the steady-state
stability limit. The limiting equipment/facility, or the bus with
voltage violation, or even the binding contingency may not occur in
the two areas involving power transfers. To address this issue, a
comprehensive modeling of the interconnected power system is
necessary for the development of an effective on-line PTC
method.
Real-Time Static-Security Constrained PTC Method
[0090] We describe our invented method for computing real-time
static security constrained power transfer limit (i.e. real-time
static PTL) with respect to a specified generation/load variation
vector, given a proposed power transaction or a proposed
simultaneous power transactions such as (i) a point-to-point MW
transaction, or (ii) a slice-of-the-system sale, or (iii) a network
service, or (iv) a reactive ancillary service, and the following
information: [0091] (1) a base case power system model with control
devices, reactive power generation limits, schemes of real power
dispatches, say due to participation factor, etc. . . . [0092] (2)
the current operating condition (obtained from the state estimator
and the topological analyzer), [0093] (3) operating policy, [0094]
(4) a set of credible contingencies, [0095] (5) voltage
constraints, thermal-limit constraints, steady-state stability
limit constraints, and [0096] (6) transient stability
constraints.
[0097] The real-time method of the invention computes the
static-security constrained PTC (i.e. static PTC) for the proposed
power transaction of the interconnected system with the following
control laws and satisfying all the constraints stated above.
Control Law
[0098] The real-time method of the invention allows the
participation of generators, loads, ULTC taps, phase-shifter
settings, shunt capacitors, and DC links as controls to maximize
available transfer capability. The control laws can be classified
as active control and passive control, where active control laws
are the control laws whose objective function is to maximize power
transfer capability through their control actions while passive
control laws are the control laws whose objective function is to
remove various types of security violations through their control
actions which can also increase power transfer capability.
[0099] The actions of active control laws can be formulated as a
constrained optimization problem whose objective function is the
transfer capability while the actions of passive control laws can
be formulated as a constrained optimization problem whose objective
function is not the transfer capability.
Identifying Binding Contingencies and Binding Constraints
[0100] It is important for the process of computing available
transfer capability to take into account all credible
contingencies. A simultaneous transfer capability solution can be
regarded as secure only if it can sustain all credible contingency
cases. The strategy of using effective schemes to rank all credible
contingencies and of applying detailed analysis programs only to
critical contingencies is widely accepted.
[0101] Adopting this strategy, the real-time method employs three
look-ahead ranking schemes for identifying critical contingencies
in terms of three static security constraints; i.e. thermal limits,
voltage limits and steady-state stability limits. With these
ranking schemes, the real-time method has the ability to: [0102]
(1) identify top binding contingencies, [0103] (2) find the
associated binding constraints, and [0104] (3) compute the
corresponding simultaneous available transfer capability.
Three Fast Look-Ahead Schemes
[0105] Three fast and yet accurate look-ahead estimators which can
identify and rank critical contingencies in the context of static
security assessments are incorporated into the real-time method.
One look-ahead estimator serves to rank the set of all credible
contingencies in terms of load (or generation/load) to their branch
MVA violations (i.e. thermal limit violations) and to identify the
top few critical contingencies for thermal limit violation. Another
look-ahead estimator ranks the set of all credible contingencies in
terms of their load margins to system collapse (i.e. steady-state
stability limit) and identifies the top few critical contingencies
for violating steady-state stability limit. The third estimator
ranks all credible contingencies in terms of their load margins to
bus voltage violation and identifies the few top critical
contingencies for voltage violation. These three look-ahead
estimators are briefly described in the next section.
[0106] Given (i) the current operating condition (obtained from the
state estimator and the topological analyzer), (ii) a proposed
power transaction or a proposed set of simultaneous power
transactions, (iii) a base case power system model with control
devices, reactive power generation limits, schemes of real power
dispatches, say due to participation factor, etc. (iv) and voltage
constraints, thermal-limit constraints, steady-state stability
limits (v) a credible contingency from a contingency list, the
three look-ahead estimators estimate the following three load
margins to the three static security limits, along the proposed
power transaction vector b for the parameterized power system
(parameterized along the direction of the proposed power
transaction) for the power system subject to the contingency.
[0107] FIG. 3 shows diagrams of the proposed three schemes for
ranking a list of contingencies in terms of three types of load
margins--nose-point, voltage limit and thermal limit. These load
margins are: [0108] (1) the nose-point load margin, say
.lamda..sup.n, to measure the distance (MW and/or MVAR) between the
current operating point to the nose point of the parameterized
power system subject to the contingency, [0109] (2) a voltage-limit
load margin, say .lamda..sup.v, to measure the distance (MW and/or
MVAR) between the current operating point to the state of the
parameterized power system subject to the contingency at which the
voltage limit constraint at some bus is violated, and [0110] (3) a
thermal-limit load margin, say .lamda..sup.t, to measure the
distance (MW and/or MVAR) between the current operating point to
the state of the parameterized power system subject to the
contingency at which the thermal limit constraint of some branches
is violated.
[0111] Each of the above three load margins is then applied to rank
the contingency list for the following three categories: [0112]
Contingency ranking for steady-state limit, [0113] Contingency
ranking for voltage violation, and [0114] Contingency ranking for
thermal violation.
[0115] A list of top-ranked contingencies can thus be composed by
selecting the top-ranked contingencies from each category.
[0116] Apply the continuation power flow (CPFLOW) method to each
top-ranked contingency to obtain the so-called P-V curve, or P-Q-V
curve and find the load margins to the steady-state limit, voltage
violation point and the thermal violation point. The smallest one
is the load margin of the top-ranked contingency.
Solution Method
[0117] The solution method for the real-time method of the
invention to evaluate the static PTC of an interconnected power
system with respect to a set of proposed power transactions subject
to static security constraints is presented below. [0118] Stage 1:
Initialization: Build the power transfer vector to represent
(mathematically) the proposed power transfer transaction and form
the parameterized power flow equations by incorporating the power
transfer vector b into the base-case power flow equations. [0119]
Stage 2: Contingency Ranking for Static Security Violation [0120]
Stage 3: Compute first-contingency PTC and identify the
corresponding binding contingency. [0121] Stage 4: Rank
Contingency-constrained PTCs and FCITCs [0122] Stage 5: Output
Analysis
[0123] A detailed description of the steps in each stage is
described below.
Stage 1: Initialization
[0124] 1.1 Build the power transfer vector b to represent
(mathematically) the proposed power transfer transaction. [0125]
1.2 Form the parameterized power flow equations by incorporating
the power transfer vector b into the base-case power flow
equations: f(x)-.lamda.b=0 [0126] 1.3 Initialize the parameter,
(i.e. generation/load condition number) .lamda. by setting
.lamda.=.lamda.to the base case.
Stage 2: Contingency Ranking for Static Security Violation
[0126] [0127] 2.1 Use a look-ahead scheme to rank the set of
contingencies L in terms of branch MVA violation. Let the ranked
set of contingencies be L(mva). [0128] 2.2 Use a look-ahead scheme
to rank the set of contingencies L in terms of bus voltage
violation. Let the ranked set of contingencies be L(volt). [0129]
2.3 Use a look-ahead scheme to rank the set of contingencies L in
terms of load margin. Let the ranked set of contingencies be
L(margin)
Stage 3: Compute First-Contingency PTC and Identify the
Corresponding Binding Contingency.
[0129] [0130] 3.1 Select the top N.sub.a contingencies from the
ordered set L(mva), the top N.sub.b contingencies from the ordered
set L(volt), and the top N.sub.c contingencies from the ordered set
L(margin). Renumber these contingencies into l.sub.1, l.sub.2 . . .
, l.sub.N.sub.a.sub.+N.sub.b.sub.+N.sub.c and if there are any sets
of duplicate contingencies, eliminate all but one of each set of
duplicate contingencies. Define a new set
L.sub.static.tangle-solidup.{l.sub.0, l, l.sub.N.sub.total}, where
l.sub.0 represents the base case power system. [0131] 3.2 For each
contingency in L.sub.static, for example l.sub.i, i=0, 1, 2, . . .
, total, do steps 3.2.1.about.3.2.4: [0132] 3.2.1 Set j=0 [0133]
3.2.2 Use CPFLOW to compute the solutions of the parameterized
power flow equations under contingency l.sub.g for each
generation/load condition number
.lamda..sub.j=.lamda..sub.j+.DELTA..lamda..sub.j, where
.DELTA..lamda..sub.j=0 if j=0; otherwise .DELTA..lamda..sub.j is
determined by the step-size control in CPFLOW. If the
post-contingency power flow solution [X(l.lamda.]) satisfies the
following static security constraints [0134] voltage:
V.ltoreq.V(l.sub.v.lamda..sub.j).ltoreq.V.sup.M [0135] line
current: I.sup.m.ltoreq.I(l.sub.v.lamda..sub.j).ltoreq.I.sup.M
[0136] facility loading: g(l.sub.v.lamda..sub.j).ltoreq.0 [0137]
then set j=j+1 and repeat Step 3.2.; otherwise, set Cbind=the
corresponding violated constraints and go to Step 3.2.3. [0138]
3.2.3 If |.lamda.-.lamda..sub.j-1|<g, go to Step 3.2.4;
otherwise, set
[0138] ? = ? 2 ? indicates text missing or illegible when filed
##EQU00005## [0139] and use CPFLOW to compute the solutions of the
parameterized power flow equations under contingency l.sub.i for
the generation/load condition number .lamda..sub.j= .lamda..sub.j.
If the post-contingency power flow solution X(l, .lamda.) satisfies
the static security constraints, then set .lamda..sub.j-1=
.lamda..sub.j and repeat Step 3.2.3; otherwise set .lamda..sub.j=
.lamda..sub.j, and Cbind=the corresponding violated constraints and
go to Step 3.2.3. [0140] 3.2.4 Record the contingency l.sub.j, the
generation/load condition number .lamda..sub.j=.lamda..sub.j-1 the
corresponding violated constraints CV.sub.j. Hence, the
(first-contingency) available transfer capability under contingency
l.sub.j is .lamda..sub.j-.lamda.with the binding constraint
CV.sub.j. [0141] 3.2.5 If t<N.sub.total, set i=i+1 and go to
Step 3.2.1; otherwise, go to Stage 4.
Stage 4: Rank Contingency-Constrained PTCs and FCITCs:
[0141] [0142] 4.1 Rank the set L.sub.static according to each value
.lamda..sub.j obtained in Step 3.2.4 and let the ranked contingency
set be L.sub.static=(l.sub.1, l.sub.2, . . . , l.sub.total) such
that .lamda..sub.1.gtoreq. .lamda..sub.2.gtoreq. . . . .gtoreq.
.lamda..sub.total. [0143] 4.2 The first-contingency PTC (or FCITC)
subject to static voltage stability constraints and static security
constraints of the contingency set L is .lamda..sub.total=(
.lamda..sub.total-.lamda..sub.0), the binding contingency
l.sub.total and the associated violated constraint is CV.sub.total.
[0144] 4.3 The PTC, under contingency I.sub.j, is .lamda..sub.j=(
.lamda..sub.j-.lamda..sub.0) with the binding constraint CV.sub.j,
for j=1, 2, . . . , total-1.quadrature.
Stage 5: Output Analysis
[0144] [0145] Output the PTC, FCITC for the power system with the
proposed power transactions under each binding contingency and the
associated violated constraints. PTC can be expressed in a number
of ways. [0146] It can be expressed on terms of the amount of PTC
between sending areas and receiving areas. [0147] On some
occasions, it is useful from monitoring and control viewpoint to
represent PTC in terms of pre-contingency interface power flows
(i.e. the base-case interface power flows) of some transmission
interface.
[0148] We explain the physical meaning of the value .lamda..sub.j
in Stage 4 of the proposed solution algorithm as the
transaction-dependent PTC for the power system subject to the
contingency, say j.
[0149] Physically, if .lamda..sub.j is greater than 1.0, then it
means that the transmission network is able to transfer the
proposed power transactions in a reliable manner, should the
contingency j occur. In addition, the (normalized) operating margin
of the power system with the proposed power transactions is
.lamda..sub.j-1.0.
[0150] On the other hand, the transmission network is unable to
transfer the proposed power transactions, should the contingency j
occur, if .lamda..sub.j is less than 1.0. In this case, the amount
of reliable power transfer is .lamda..sub.j% of the proposed power
transactions. For example, if .lamda..sub.j equals 0.7, then the
available transfer capability for the proposed power transactions
is 70% of the proposed power transactions.
[0151] This (normalized) operating margin can be translated into
operational guidelines as follows: the system can reliably transfer
the proposed power transaction. In addition, the transmission
network can transfer additional ( .lamda..sub.j-1.0) % of the
original proposed power transaction in a reliable manner.
[0152] The static PTC can be expressed in several ways. It is
sometimes useful to represent the static PTC in terms of
pre-contingency interface power flow (i.e. the base-case interface
power flow) at the limit point. The calculated system-wide static
PTC is then mapped into each interface static PTC.
Numerical Studies
[0153] We consider a 15005-bus interconnected power system
containing about 2400 generators, 16,000 transmission lines, 8,000
loads, 4000 fixed transformers, 2400 fixed shunts, 3000 ULTC
transformers, 800 switchable shunts, and other control devices such
as fixed and ULTC phase shifters, etc.
[0154] Given a base case of the interconnected power system with a
secure operating point, a proposed power transaction described by
transmitting 1300 MW real power from area A to area B by decreasing
all the real power generations of area B uniformly to zero (24
generators are scaled down to 0 MW) and increasing real power
generations of area A uniformly to supply the loads of Area B (the
area-wide generation of Area A is scaled properly), we apply the
real-time method to evaluate the real power transfer capability
from area A to area B of the interconnected power system subject to
a contingency list which is a set of transmission line or generator
outages.
[0155] Three cutsets of 500 KV transmission lines were selected and
the corresponding sum of the line flows was defined as the
interface line flows.
[0156] In this numerical study, the PTC is expressed in terms of
either (i) power transfer capability between the sending area and
the receiving area, or (ii) the pre-contingency power flow of the
three interface flows.
[0157] The three fast look-ahead estimators were applied to the
contingency list. The top five most serious contingencies captured
by each look-ahead estimator and the corresponding estimated load
margin are listed in Table 1, Table 2 and Table 3, respectively. In
these three tables, the contingency with the sign * is a generator
trip.
TABLE-US-00001 TABLE 1 The five most serious contingencies
according to their impacts on the load margins to the stead-state
stability limit and the corresponding load margin. Estimated Load
margin Estimated Contingency (MW) Lambda 32-6830 933 0.728
4364-6831 1043 0.808 85-4323 1053 0.81 *4523 1053 0.81 *4496 1057
0.813
TABLE-US-00002 TABLE 2 The five most serious contingencies
according to their impacts on the load margins to the thermal limit
and the corresponding load margin. Estimated Contingency Estimated
margin (MW) Lambda 89389-89392 194 0.149 *289 566 0.435 89394-104
681 0.524 *7498 746 0.574 *89418 785 0.604
TABLE-US-00003 TABLE 3 The five most serious contingencies
according to their impacts on the load margins to the stead-state
stability limit and the corresponding load margin. Estimated
Contingency Estimated margin (MW) Lambda 4364-6831 680 0.523
85-4323 748 0.575 32-6830 754 0.58 *7498 759 0.584 89386-89387 759
0.584
[0158] Since 4 of 15 contingencies are redundant, there are only 11
contingencies that require further study. A detailed analysis based
on the continuation power flow (CPFLOW) was performed for each of
these 11 contingencies to compute the PTC and to identify the
corresponding binding constraint. Note that the participation of
all control devices and the physical constraints of these control
devices are taken into account in the process of continuation power
flow study.
[0159] The final results of ATC, which is the difference between
the PTC and the current power flow with respect to the proposed
power transaction along with the corresponding binding contingency
and the corresponding binding constraints are shown in Table 4.
TABLE-US-00004 TABLE 4 Output Analysis of PTC computation
Pre-contingency Interface power flow The top eight of serious
Contingency three interfaces (MW) Corresponding Binding Constraints
Contingency Location East Central West ATC (MW) Type location Base
Case Base Case 5552 2247 4473 913 Voltage 7084 The most serious
89389-89392 5422 2203 4445 234 Thermal 3687-3337 2nd most serious
89394-104 5478 2218 4452 584 Thermal 37-276, 37-277 3rd most
serious 4364-6831 5531 2237 4465 820 Voltage 6807, 6808, 7804 4th
most serious 32-6830 5537 2240 4467 845 Voltage 6807, 6808, 7804
5th most serious *7498 5538 2241 4468 857 Thermal 37-276, 37-277
6th most serious 85-4323 5541 2242 4468 869 Voltage 7804 7th most
serious *4496 5543 2243 4469 883 Thermal 37-276, 37-277 8th most
serious 89386-89387 5549 2246 4472 898 Thermal 37-276, 37-277
[0160] The numerical simulation shows that the ATC for the proposed
power transaction, under the assumed set of contingencies, is 234
MW between the sending area and the receiving area (instead of 1300
MW). The corresponding contingency (i.e. 89389-89392) is the
binding contingency. Equivalently, the ATC of the proposed
transaction is 5422 MW for the east interface, 2203 MW for the
central interface, and 4445 MW for the west interface.
[0161] It is interesting to note that the constrained east
interface line flow under this contingency is the smallest among
the constrained east interface line flows of the contingencies
considered. This is also true for the constrained central interface
line flow and the constrained west interface line flow.
[0162] The real-time method of the invention can compute each ATC
with the corresponding binding contingency as a by-product and the
associated violated constraint in an `increasing` order as shown in
Table 4. This piece of information is useful for decision-making
personnel to take a proactive approach to measure the transfer
capability of the network.
[0163] For instance, the ATC of the study system without the
consideration of the contingency (89389-89392) is 584 MW. If the
probability of the occurrence of contingency 89389-89392 is low,
then it may be reasonable to post the ATC as 584 MW and, in the
meantime, a remedy control scheme can be prepared in advance should
contingency 89389-89392 occur.
[0164] Likewise, the ATC of the study system without the
consideration of contingencies 89389-89392 & 89394-104 is 820
MW. If the probability of the occurrence of either contingency
89389-89392 or 89394-104 is low, then it may be reasonable to post
the ATC as 820 MW and, in the meantime, a remedy control scheme can
be prepared in advance should contingencies 89389-89392 and/or
89394-104 occur.
[0165] It should be also pointed out that this real-time method
also allows (via the establishment of Table 4) a probabilistic
treatment of each contingency and the associated risk management.
Economic factors can also be linked to Table 4.
Real-TimeStatic PTC in 2-Dimensional Nomogram
[0166] A static PTC nomogram is a two-dimensional display of static
PTC in terms of two interface flows. Nomograms provide vital
information for power system operators to operate power systems
within power transmission static security limits and with a
`comfort zone`. A nomogram always involves two interface paths. In
computing a nomogram, we first need to associate one interface path
with the X axis and the other interface path with the Y axis. Then
we separate all source generators involved in the stress pattern
into two groups. The source group that is responsible for the flow
change in the X axis path is classified as group X, which is
denoted as G.sub.1. The source group that is responsible for the
power flow change in the Y axis path is classified as group Y,
which is denoted as G.sub.2.
[0167] We compute the static PTC nomogram in the following way. We
at first create two independent base generation vectors for
b.sub.g1, b.sub.g2 G.sub.1 and G.sub.2 respectively. Then, we
create two independent coefficients for a.sub.1, a.sub.2
respectively. The overall generation vector considering both source
groups will be:
b.sub.g=a.sub.1b.sub.g1+a.sub.2b.sub.g2 (6)
[0168] By assigning a.sub.1, a.sub.2 different values, we create a
family of generation/load stress patterns, which spans the entire
feasible generation/load stress space. For each generation/load
stress pattern, we use the CPFLOW to compute the voltage stability
load margin (i.e. the boundary of the nomogram along the stress
pattern).
[0169] The proposed solution method to compute the static PTC
nomogram is as follows: [0170] Step 1: Separate source generators
into two groups G.sub.1 and G.sub.2 and assign a.sub.1=0 and
a.sub.2=1 [0171] Step 2: Compute b.sub.g using the equation:
[0171] b.sub.g=a.sub.1b.sub.g1+a.sub.2b.sub.g2 (6) [0172] Step 3:
Use the proposed real-time method to compute the (one-dimensional)
system-wide static PTC and the corresponding interface static PTC's
along the direction b.sub.g. [0173] Step 4: Assign different values
for a.sub.1 and a.sub.2 in the equation of step 2 and repeat Step
2: Compute b.sub.g using the equation:
[0173] b.sub.g=a.sub.1b.sub.g1+a.sub.gb.sub.g2 (6) [0174] to Step 3
to compute all points on the nomogram boundary (i.e. curve). [0175]
Step 5: Export the static PTC nomogram curve and the corresponding
limiting contingency of each computed point on the nomogram
boundary.
[0176] FIG. 4 shows a graph of how a stress pattern spans the
entire feasible generation/load stress space.
[0177] The static PTC nomogram can be expressed in several ways. It
is sometimes useful to represent the static PTC nomogram in terms
of pre-contingency interface power flow (i.e. the base-case
interface power flow) at the limit point. The calculated
system-wide static PTC nomogram is then mapped into each interface
static PTC nomogram. FIG. 5 shows diagrams of how a system-wide
static PTC nomogram is mapped into each pair of tie-line interfaces
static PTC nomogram.
Real-Time Static ATC Determination System
[0178] The real-time ATC is the difference between the real-time
PTC and the current actual power flow. To provide a real-time
static ATC (i.e. ATC subject to static security constraints and
voltage security constraints), it is necessary to have some
real-time information regarding a system's operating conditions
This invention proposes to apply a wide-area measurement system
(WAMS) such as phasor measurement units (PMUs) installed at
selected tie-lines and buses to obtain the required real-time real
power and reactive power information.
[0179] One central topic in the area of wide-area measurement is
the utilization of this new type of measurement (as opposed to
traditional SCADA measurements). Phasor data, precisely
time-synchronized data at a high data rate, provide a wide-area
view of current power system conditions. To fill the gap between
real-time phasor measurements and real-time operation applications,
we propose to develop an integrated system which contains a
wide-area measurement system and the real-time PTC system for an
accurate determination of real-time PTC. This real-time PTC
determination ensures power system security and reliability while
offers better power system asset utilization and economic
benefits.
[0180] FIG. 6 shows the tie-line power flow of interface #1 is
measured by PMU's placed across interface #1 while the static PTC
of interface #1 is computed by the proposed method for computing
the real-time static PTC. The difference between the static PTC and
the real-time tie-line power flow is the real-time static ATC.
[0181] FIG. 7 shows the tie-line power flow of interface #i is
measured by PMU's placed across interface #i while the tie-line
power flow of interface #j is measured by PMU's placed across
interface #j. The static PTC nomogram for interfaces #i and #j is
computed by the invented method. The distance between the static
PTC nomogram and the real-time tie-line power flows is the
real-time static ATC in 2-dimension.
[0182] Given an operating point (derived from a state estimator), a
network topology, a set of pre-determined interfaces and a
contingency list associated with each interface, we develop a
PMU-assisted, real-time static ATC determination system for each
interface. The output of this system can be expressed as the
following: [0183] Real-time Static ATC in One-dimensional maps
(shown in FIG. 6), [0184] Real-time Static ATC in Two-dimensional
maps (i.e. in nomogram, as shown in FIG. 7).
[0185] The architecture of the invented method for determining the
real-time static ATC is shown in FIG. 8 and in FIG. 9 respectively
for different expressions of ATCs.
[0186] There are four key components in this real-time static ATC
determination system: [0187] (1) stator estimator and network
topology analyzer from an energy management system; [0188] (2) the
invented real-time static power transfer capability measurement
system; [0189] (3) the real-time measurement units, PMUs, placed
various locations including a set of pre-determined interfaces; and
[0190] (4) the real-time ATC display system with both
one-dimensional and two-dimensional ATC monitoring system.
[0191] It should be pointed out that the solution methods of the
invented system can also determine the top-ranked interface static
power transfer limit of each selected interface under the
contingency list associated with each interface.
[0192] This real-time static ATC determination system has the
following features: [0193] (1) The real-time static security ATC
calculation methodology determines the top-ranked system-wide power
transfer limits subject to static security constraints of a
contingency list. [0194] (2) The system identifies, for each
top-ranked power transfer limit, the corresponding limiting
contingency and the corresponding binding constraint. [0195] (3)
The system maps each top-ranked system-wide power transfer limit
into the power transfer limit of each selected tie-line interface
under the contingency. [0196] (4) The real-time measurement of
power flow across each selected tie-line interface is obtained from
the installed PMUs. For each limiting contingency, the difference
between the corresponding power transfer limit and the current
power transfer is the real-time available transfer capability of
the system associated with the top limiting contingency and the
corresponding binding constraint expressed as the power flow across
each interface.
Real-Time Dynamic PTC
[0197] In the following discussion, we define the real-time dynamic
power transfer capability of a power system.
[0198] The transient-stability-limit power transfer capability
(PTC), or termed dynamic PTC is defined as the (minimum) distance
(i.e. load margin in terms of MW and/or MVAR) from the current
real-time operating point to the state vector of the base-case P-V
curve, along a stress pattern (or a given power transaction) on
which at least one contingency, from a contingency list, would
result in transient instability.
[0199] We note that the dynamic PTC should be smaller than the
nose-point load margin of the base-case power system since the
transient-stability-limit load margin is not defined when its value
is greater than the nose-point load margin of the base-case power
system. The task of computing the transient-stability-limit load
margin with respect to a set of credible contingencies is rather
challenging.
[0200] In this invention, we develop a methodology, termed the
BCU-limiter, which can quickly and accurately compute the PTC
limited by the transient stability of credible contingencies (i.e.
the real-time dynamic PTC). This BCU-limiter computes, given a
proposed power transaction, the amount of power transfers a power
system can withstand before its transient stability limit is
reached.
[0201] In addition, the BCU-limiter can rank a given list of
contingencies, in terms of their load margins, to transient
stability limits and compute the corresponding PTC. This
BCU-limiter is an integration of the BCU methods, the BCU
classifiers, the continuation power flow (CPFLOW) method and a
time-domain simulation method.
[0202] Given an operating point, the BCU-limiter not only performs
power system dynamic security assessments and ranking but also
computes the PTC limited by the transient stability of credible
contingencies.
[0203] The amount of required calculation is huge and the following
requirements are important for computing transient stability
constrained PTC under a list of contingencies. [0204] [1] Accuracy:
the limiting contingencies to which the PTC is subject must be
captured. [0205] [2] Performance: the PTC computation involves
transient stability assessment at multiple loading conditions on
the base-case P-V curve. This fact, together with the fact that the
size of contingency list can be very large, imply that PTC
computation indeed requires significant amount of computational
efforts.
[0206] This invention designs an effective search algorithm that
enables one to fast determine real-time dynamic PTC. The operating
points chosen from the P-V curves on which the transient stability
analysis of a contingency list is to be performed has a huge
influence on the efficiency of the overall computation engine. We
next propose an energy-margin-based search method to select the
next operating point between two known operating points on a P-V
curve.
Energy-margin-based Bisection Search Method
[0207] Step 1: Apply the BCU method to compute the energy margin of
contingency i at the base-case .lamda.=.lamda..sub.0. Let the
energy margin of contingency i be W.sub.i.sup.(.lamda..sup.0.sup.).
If W.sub.i.sup.(.lamda..sup.0.sup.)>0, then contingency i is
stable, otherwise, it may be unstable. [0208] Step 2: Apply the BCU
method to compute the energy margin of contingency i at another
loading condition, say .lamda.=1. Let the energy margin of
contingency i be W.sub.i.sup.(.lamda..sup.1.sup.). If
W.sub.i.sup.(.lamda..sup.1.sup.)<0 then contingency i is
unstable at the loading condition .lamda.=.lamda..sub.1. Without
loss of generality, it is assumed that
W.sub.i.sup.(.lamda..sup.1.sup.)<0. [0209] Step 3: The power
transfer limit (PTL) relative to contingency i lies between the two
loading conditions .lamda..sub.0 and .lamda..sub.1. [0210] Step 4:
There exist several one-dimensional search algorithms, for
example,
[0211] Bracketing and Bisection algorithms, secant algorithms,
Ridder's algorithm etc. to identify the PTL subject to contingency
i. Here, we illustrate the Ridder's algorithm to find the root of
the following equation
W.sub.i(.lamda.)=0, with W.sub.i(.lamda..sub.1)<0 and
W.sub.i(.lamda..sub.1)>0 and .lamda..epsilon.[.lamda..sub.0,
.lamda..sub.1] [0212] where W.sub.i(.) is an energy function for
contingency i. [0213] Step 5: Compute a new loading condition
[0213] ? = .lamda. 0 + .lamda. 1 2 ? indicates text missing or
illegible when filed ##EQU00006## [0214] and compute the energy
margin at the new loading condition W.sub.i(.lamda..sub.2). [0215]
Step 6: Compute the next loading level
[0215] ? - ? + ? ? - W .quadrature. ( .lamda. 0 ) W .quadrature. (
.lamda. 1 ) ? indicates text missing or illegible when filed
##EQU00007## [0216] Step 7: The next loading condition to be
evaluated for transfer stability assessment is at
.lamda..sub..quadrature.=.lamda.
[0217] Another one-dimensional search method for implementing Step
4 of the above algorithm is the golden bisection method, which is
an one dimensional search method used for finding the optimal
solution of a real-valued unimodal function. A unimodal function
F(x) has the property that there is an unique x* on a given
interval [a,b] such that F(x*) is the only minimum of F(x) on the
interval, and F(x) is strictly decreasing for x.ltoreq.x* and
strictly increasing for x.gtoreq.x*. The significance of this
property is that it enables us to refine an interval containing a
solution by computing sample values of the solution within the
interval and discarding portions of the interval according to the
function values obtained.
Computing Real-Time Dynamic PTC
[0218] We now describe a real-time methodology, termed BCU-limiter,
to compute real-time dynamic PTC. [0219] Step 1: Apply the
Continuation Power Flow (CPFLOW) method to compute the P-V curve
for the base-case power system for a given generation/load
variation pattern (i.e. for a proposed power transaction). [0220]
Step 2: Apply the TEPCO-BCU method described below to the base-case
operating point to perform transient stability analysis of the
operating point subject to a contingency list. [0221] Step 3: If
there is an insecure or critical contingency at the (current)
base-case operating point, then the dynamic PTC is zero for the
proposed power transaction, otherwise, set the base-case operating
point as the lower bound of the dynamic PTC and record the
corresponding critical contingencies and their corresponding energy
margin, and continue to the next step. [0222] Step 4: Apply the
TEPCO-BCU method to the base-case nose point to perform a transient
stability analysis subject to the entire contingency list. [0223]
Step 5: If there is no insecure or critical contingency at the
base-case nose point, then the dynamic PTC is greater than the
static PTC for the proposed power transaction, output the dynamic
PTC as the same value of static PTC and stop; otherwise, set the
base-case nose point as the upper bound of the dynamic PTC and
record the corresponding insecure and critical contingencies and
their corresponding energy margin, and continue to the next step.
[0224] Step 6: Select a loading condition on the P-V curve between
the lower bound and the upper bound of the dynamic PTCs based on
the energy-margin golden bisection search algorithm. [0225] Step 7:
Apply the TEPCO-BCU engine to the selected loading condition of
Step 6 to perform transient stability analysis subject to the
newly-updated contingency list (such as a selected set of
contingencies based on the insecure and critical contingencies at
both the upper bound operating point and lower bound operating
point). [0226] Step 8: If one or more insecure contingencies are
detected, set the current loading condition as the upper bound of
the dynamic PTC; otherwise, update the lower bound of dynamic PTC
by the currently selected loading condition. If the difference
between the lower bound and upper bound of the dynamic PTC is
larger than a specified number, then go to Step 6. [0227] Step 9:
Export the top-limiting contingencies and compute the corresponding
dynamic PTCs.
[0228] We note that the TEPCO-BCU method is the method described in
the following patents, which are incorporated herein by reference:
[0229] U.S. Pat. No. 7,483,826; "Group-Based BCU Methods for
real-time Dynamical Security Assessments and Energy Margin
Calculations of Practical Power Systems" Date of patent, Jan. 27,
2009 (Inventors: Hsiao-Dong Chiang, Hua Li, Yasuyuki Tada, Tsuyoshi
Takazawa, Takeshi Yamada, Atsushi Kurit, and Kaoru Koyanagi) [0230]
U.S. Pat. No. 7,761,402; "Group-Based BCU Methods for real-time
Dynamical Security Assessments and Energy Margin Calculations of
Practical Power Systems" Date of patent, Jul. 20, 2010 (Inventors:
Hsiao-Dong Chiang, Hua Li, Yasuyuki Tada, Tsuyoshi Takazawa,
Takeshi Yamada, Atsushi Kurit, and Kaoru Koyanagi) [0231] Japan
Patent 4,276,090; "Method and System for real-time Dynamical
Screening of Electric Power System" Date of Patent, Mar. 13, 2009
(Application number 2003-586902, filing date Apr. 21, 2003),
(Inventors: Hsiao-Dong Chiang, Atsushi Kurita, Hiroshi Okamoto,
Ryuya Tanabe, Yasuyuki Tada, Kaoru Koyanagi, and Yicheng Zhou)
[0232] Japan, Patent 4,611,908; "Group-Based BCU Methods for
real-time Dynamical Security Assessments and Energy Margin
Calculations of Practical Power Systems" Date of Patent, Oct. 22,
2010 (Application number 2006-031327, filing date Feb. 8, 2006),
(Inventors: Hsiao-Dong Chiang, Hua Li, Yasuyuki Tada, Tsuyoshi
Takazawa, Takeshi Yamada, Atsushi Kurit, and Kaoru Koyanagi) [0233]
Peoples of Republic of China, Patent ZL 038,089,55.6; "Method and
System for real-time Dynamical Screening of Electric Power System"
Date of Patent, Dec. 10, 2008 (filing date Apr. 21, 2003),
(Inventors: Hsiao-Dong Chiang, Atsushi Kurita, Hiroshi Okamoto,
Ryuya Tanabe, Yasuyuki Tada, Kaoru Koyanagi, and Yicheng Zhou)
[0234] The TEPCO-BCU engine is composed of two major functions:
[0235] [1] Fast contingency screening function. It processes the
full set of credible contingencies at a given system condition.
Each contingency will be identified as potentially unstable or
definitely stable. Definitely stable contingencies are then
assigned with appropriate energy function values (i.e. stability
margins) according to BCU method and are eliminated from further
stability analysis. Potentially unstable contingencies are then
sent to the detailed time-domain stability analysis module for
detailed stability assessment. The output of this fast contingency
screening module will be a short list of the following: [0236] (a)
Potential unstable contingencies with an energy margin [0237] (b)
Critical stable contingencies with an energy margin [0238] [2].
Detailed transient stability analysis function. This function
mainly employs the time-domain simulation method for detailed
transient stability analysis to accurately assess the
stability/instability property of the screened (i.e. potentially
unstable) set of contingencies so that the transient stability of
the screened contingencies can be determined.
[0239] The dynamic PTC can be expressed in several ways. It is
sometimes useful to represent the dynamic PTC in terms of
pre-contingency interface power flow (i.e. the base-case interface
power flow) at the limit operating point. The system-wide dynamic
PTC is then mapped into each interface dynamic PTC.
Numerical Example
[0240] The 65-generator system represents a subsystem of a major
interconnected grid in the North America. This subsystem is
composed of nine areas with 1135 buses and 2216 transmission lines.
The base-case area interchange power flows are graphically
displayed in FIG. 10.
[0241] There are seven tie lines between area 1 and area 2 with
interchange power flow of 1207.67 MW and -217.47 MVar from Area 1
and Area 2. One good of this study is to find the real power
transfer limit (i.e. PTC) from area 1 to area 2 under the transient
stability constraint with the following operating scenario:
[0242] Area 2 generators decreases from the base-case value
17030.79 MW to 12091 MW; uniformly among all the generators in Area
while Area 1 generation uniformly increases from 19365.88 MW to
24400 MW to compensate the power deficit in Area 2. The
transmission losses incurred from this power transfer from Area 1
to Area 2 are compensated by the Area slack buses in Area 1 and
Area 2.
[0243] The system-wide dynamic PTC and the interface-flow dynamic
PTC between Area 1 and Area 2 are to be computed. The
interface-flow between Area 1 and Area 2 is defined as the sum of
the power flows on the seven tie lines. The treatment of reactive
power limits, real power generations due to participation factors,
switchable capacitors and transformer tap adjustment are handled by
the Continuation Power Flow. The contingency list contains fourteen
contingencies related to the seven tie lines between Area 1 and
Area 2. The faults are 3-phase balanced faults occurring at both
end buses of the transmission line.
[0244] The P-V curve traced by Continuation Power Flow along the
direction of power transfers between Area 1 and Area 2 reaches the
corresponding nose point at which the real interface-flow is 3263
MW. While this nose point is often referred to as the maximum power
transfer point or maximum loading point, it is evident that this
maximum power transfer point is not a feasible operating point from
the static viewpoints of voltage-limit, thermal-limit or the
dynamic viewpoint of transient stability. In other words, the
maximum power transfer point usually does not represent the static
PTC or the dynamic PTC.
[0245] FIG. 11 shows the accuracy of BCU-limiter, as compared with
the time-domain approach on twelve contingencies in terms of error.
The errors are all between 0% and 3.2%. It shows the accuracy and
conservativeness nature of the invented BCU-limiter.
Real-Time Dynamic PTC in 2-Dimensional Nomogram
[0246] A dynamic PTC nomogram is a two-dimensional display of
dynamic PTC in terms of two interface flows. Nomograms provide
vital information for power system operators to operate power
systems within power transmission dynamic security limits and with
a `comfort zone`.
[0247] A nomogram always involves two interface paths. In computing
a nomogram, we first need to associate one interface path with the
X axis and the other interface path with the Y axis. Then we
separate all source generators involved in the stress pattern into
two groups. The source group that is responsible for the flow
change in the X axis path is classified as group X, which is
denoted as G.sub.1. The source group that is responsible for the
power flow change in the Y axis path is classified as group Y,
which is denoted as G.sub.2.
[0248] We compute the dynamic PTC nomogram in the following way. We
at first create two independent base generation vectors b.sub.g1,
b.sub.g2 for G.sub.1 and G.sub.2 respectively. Then, we create two
independent coefficients for a.sub.1, a.sub.2 respectively. The
overall generation vector considering both source groups will be
the same as equation (6). By assigning at, a.sub.1, a.sub.2
different values, we can create a family of generation/load stress
patterns, which spans the entire feasible generation/load stress
space.
[0249] For each generation/load stress pattern, we will use the
invented TEPCO-BCU-Limiter to compute the dynamic PTC (i.e. the
boundary of the nomogram along the stress pattern). The invented
solution algorithm to compute the dynamic PTC nomogram is as
follows: [0250] Step 1: Separate source generators into two groups
G.sub.1 and G.sub.2, and assign a.sub.1=0 and a.sub.2=1 [0251] Step
2: Compute b.sub.g using the equation:
[0251] b.sub.g=a.sub.1b.sub.g1+a.sub.gb.sub.g2 (6) [0252] Step 3:
Use the invented method to compute the (one-dimensional)
system-wide dynamic PTC and the corresponding interface dynamic
PTC's along the direction b.sub.g. [0253] Step 4: Assign different
values for a.sub.1 and a.sub.2 in the equation of Step 2, and
repeat Step 2: Compute b.sub.g using the equation:
[0253] b.sub.g=a.sub.1b.sub.g1+a.sub.2b.sub.g2 (6) [0254] to Step 3
to compute all points on the nomogram boundary (i.e. curve). [0255]
Step 5: Export the dynamic PTC nomogram curve and the corresponding
limiting contingency of each computed point on the nomogram
boundary.
[0256] It is sometimes useful to represent the dynamic PTC nomogram
in terms of pre-contingency interface power flow (i.e. the
base-case interface power flow) at the limit point. The system-wide
dynamic PTC nomogram is then mapped into each interface dynamic PTC
nomogram.
Real-Time Dynamic ATC
[0257] The real-time ATC is the difference between the real-time
PTC and the current (i.e. real-time) power flow. To provide a
real-time dynamic ATC (i.e. ATC subject to transient stability
constraints), it is necessary to have some real-time information
regarding a system's operating conditions.
[0258] This invention proposes to apply wide-area measurement
system (WAMS) such as phasor measurement units (PMUs) installed at
selected tie-lines and buses to obtain required real-time real
power and reactive power information. The task of determining
real-time dynamic ATC subject to dynamic security constraints is
very challenging due to the nonlinear nature of interconnected
power systems and the tremendous computation requirements of the
transient stability analysis of credible contingencies.
[0259] FIG. 12 shows tie-line power flow of interface #1 is
measured by PMU's placed across interface #1 while the dynamic PTC
of interface #1 is computed by the invented method for computing
the real-time dynamic PTC. The difference between the real-time
dynamic PTC and the real-time tie-line power flow is the real-time
dynamic ATC.
[0260] Given an operating point (derived from a state estimator), a
network topology, a set of pre-determined interfaces and a
contingency list associated with each interface, we develop a
PMU-assisted, real-time dynamic ATC determination system. There are
four key components in the invented PMU-assisted, real-time dynamic
ATC determination system: [0261] (1) stator estimator and network
topology analyzer from an energy management system, which provides
the current operating point, [0262] (2) the invented real-time
dynamic power transfer capability system, which provides the
dynamic PTC, [0263] (3) the real-time measurement units such as
PMUs, placed various locations including a set of pre-determined
interfaces, and [0264] (4) the real-time ATC display system with
both one-dimensional and two-dimensional ATC monitoring system.
[0265] The output of the PMU-assisted, real-time dynamic ATC
determination system can be expressed as the one-dimensional
dynamic PTC (see FIG. 12). The proposed architecture of the
Real-time dynamic ATC determination system in One-dimensional maps
is shown FIG. 13. In this architecture, the core computation
engines for real-time dynamic PTC determination are composed of
TEPCO-BCU methods, BCU classifiers, energy function method,
continuation power flow method, time-domain simulation method and
top-ranked contingency identification method.
[0266] The proposed architecture of the Real-time dynamic ATC
nomogram (i.e. in Two-dimensional maps) is shown in FIG. 14.
[0267] It should be pointed out that the solution methods of the
invented system can also determine the top-ranked interface dynamic
power transfer limit of each selected interface under the
contingency list associated with each interface.
[0268] This real-time dynamic ATC determination system has the
following features: [0269] (1) The real-time dynamic ATC
calculation methodology determines the top-ranked system-wide power
transfer limits subject to dynamic security constraints of a
contingency list. [0270] (2) The system identifies, for each
top-ranked power transfer limit, the corresponding limiting
contingency and the corresponding binding constraint. [0271] (3)
The system maps each top-ranked system-wide power transfer limit
into the power transfer limit of each selected tie-line interface
under the contingency. [0272] (4) The real-time measurement of
power flow across each selected tie-line interface is obtained from
the installed PMUs. For each limiting contingency, the difference
between the corresponding power transfer limit and the current
power transfer is the real-time available transfer capability of
the system associated with the top limiting contingency and the
corresponding binding constraint expressed as the power flow across
each interface.
Real-Time Static and Dynamic PTC
[0273] We now describe the invented real-time methodology to
compute real-time PTC subject to static and dynamic security
constraints, which is described as follows: [0274] Step 1: Apply
the Continuation Power Flow (CPFLOW) method to compute the P-V
curves for the base-case power system for a proposed power
transaction. [0275] Step 2: Compute the static PTC subject to
static constraints of a credible contingency list; termed as static
PTC. The corresponding operating point is termed as the (base-case)
static-security-constrained (SSC) operating limit point. Record the
corresponding limiting contingency. [0276] Step 3: Apply the
TEPCO-BCU engine to the current base-case operating point, which is
obtained from the state estimation, to perform transient stability
analysis of the operating point subject to a contingency list.
[0277] Step 4: If there is an insecure or critical contingency at
the (current) base-case operating point, then the dynamic PTC is
zero for the proposed power transaction--output the real-time
static and dynamic PTC to be zero and stop the computation.
Otherwise, set the base-case operating point as the lower bound of
the dynamic PTC and record the corresponding critical contingencies
and their corresponding energy margin and continue to the next
step. [0278] Step 5: Apply the TEPCO-BCU engine to the base-case
static-security-constrained (SSC) operating limit point to perform
transient stability analysis subject to the contingency list.
[0279] Step 6: If there is no insecure or critical contingency at
the base-case SSC operating limit point, then the dynamic PTC is
greater than the static PTC for the proposed power transaction, and
go to Step 10. Otherwise, set the base-case SSC operating limit
point as the upper bound of the dynamic PTC, record the
corresponding insecure and critical contingencies and their
corresponding energy margin, and continue to the next step. [0280]
Step 7: Select a loading condition on the P-V curve between the
lower bound and the upper bound of the dynamic PTCs based on an
energy-margin one-dimensional search method such as the golden
bisection search algorithm. [0281] Step 8: Apply the TEPCO-BCU
method to the selected loading condition of Step 6 to perform
transient stability analysis subject to the newly-updated
contingency list (such as a selected set of contingencies based on
the insecure and critical contingencies at both the upper bound
operating point and lower bound operating point). [0282] Step 9: If
one or more insecure contingencies are detected, set the current
loading condition as the upper bound of the dynamic PTC; otherwise,
update the lower bound of dynamic PTC by the currently selected
loading condition. If the difference between the lower bound and
upper bound of the dynamic PTC is larger than a specified number,
then go to Step 6. [0283] Step 10: Export the top-limiting
contingencies and the corresponding static and dynamic PTCs and
stop.
[0284] The static and dynamic PTC load margin can be expressed in
several ways. It is sometimes useful to represent the static and
dynamic PTC load margin in terms of pre-contingency interface power
flow (i.e. the base-case interface power flow) at the limit point.
The system-wide static and dynamic PTC load margin is then mapped
into each interface static and dynamic PTC load margin.
Real-Time Static and Dynamic PTC in 2-Dimensional Nomogram
[0285] We compute the static and dynamic PTC nomogram in the
following way. We at first create two independent base generation
vectors) b.sub.g1, b.sub.g2 for G.sub.1 and G.sub.2 respectively.
Then, we create two independent coefficients for a.sub.1, a.sub.2
respectively. The overall generation vector considering both source
groups will be the same as equation (6), below. By assigning
a.sub.1, a.sub.2 different values, we can create a family of
generation/load stress patterns, which spans the entire feasible
generation/load stress space.
[0286] For each generation/load stress pattern, we will use the
invented TEPCO-BCU-Limiter to compute the static and dynamic PTC
nomogram (i.e. the boundary of the nomogram along the stress
pattern). We continue this procedure for a family of
generation/load stress patterns to obtain the static and dynamic
PTC nomogram. The invented solution algorithm to compute the static
and dynamic PTC nomogram is as follows [0287] Step 1: Separate
source generators into two groups G.sub.1 and G.sub.2, and assign
a.sub.1=0 and a.sub.2=1 [0288] Step 2: Compute b.sub.g using the
equation:
[0288] b.sub.g=a.sub.1b.sub.g1+a.sub.2b.sub.g2 (6) [0289] Step 3:
Use the proposed real-time PTC method to compute the
(one-dimensional) system-wide static and dynamic PTC and the
corresponding interface static and dynamic PTC's along the
direction b.sub.g. [0290] Step 4: Assign different values for
a.sub.1 and a.sub.2 in the equation of step 2 and repeat Step 2:
Compute b.sub.g using the equation:
[0290] b.sub.g=a.sub.1b.sub.g1+a.sub.2b.sub.g2 (6) [0291] to Step 3
to compute all points on the nomogram boundary (i.e. curve). [0292]
Step 5: Export the static and dynamic PTC nomogram curve and the
corresponding limiting contingency of each computed point on the
nomogram boundary.
[0293] The static and dynamic PTC nomogram can be expressed in
several ways. It is sometimes useful to represent the static and
dynamic PTC nomogram in terms of pre-contingency interface power
flow (i.e. the base-case interface power flow) at the limit point.
The system-wide static and dynamic PTC nomogram is then mapped into
each interface static and dynamic PTC nomogram.
Real-Time Static and Dynamic ATC
[0294] The task of determining real-time static and dynamic ATC is
very challenging due to the nonlinear nature of interconnected
power systems and the tremendous computation requirements of the
line thermal limits, bus voltage limits, voltage stability
constraints and transient stability constraints of credible
contingencies. Given an operating point (derived from a state
estimator), a network topology, a set of pre-determined interfaces
and a contingency list associated with each interface, we develop a
PMU-assisted, real-time static and dynamic ATC determination
system.
[0295] FIG. 15 shows tie-line power flow of interface #1 is
measured by PMU's placed across interface #1 while the static and
dynamic PTC of interface #1 is computed by the invented method. The
difference between the real-time static and dynamic PTC and the
real-time tie-line power flow is the real-time static and dynamic
ATC.
[0296] FIG. 16 shows how the output of the PMU-assisted, real-time
static and dynamic ATC determination system can be expressed as a
two-dimensional nomogram.
[0297] FIG. 17 shows an architecture of a PMU-assisted, real-time
static and dynamic available transfer capability determination
system with one-dimensional meter displays for each interface.
[0298] FIG. 18 shows an architecture of a PMU-assisted, real-time
static and dynamic available transfer capability determination
system with two-dimensional monogram displays for each pair
interfaces.
[0299] The output of the PMU-assisted, real-time static and dynamic
ATC determination system can be expressed as an one-dimensional
meter (see FIG. 15). The output of the PMU-assisted, real-time
static and dynamic ATC determination system can be expressed as a
two-dimensional nomogram (see FIG. 16). The proposed architecture
of the Real-time dynamic ATC determination system in
One-dimensional maps is shown in FIG. 17. In this architecture, the
core computation engines for real-time static and dynamic PTC
determination are composed of TEPCO-BCU methods, BCU classifiers,
energy function method, continuation power flow method, time-domain
simulation method, top-ranked contingency identification method,
nose-point load margin estimation, voltage-limit load margin
estimation, thermal-limit load margin estimation. The proposed
architecture of the Real-time dynamic ATC nomogram (i.e. in
Two-dimensional maps) is shown in FIG. 18.
[0300] There are four key components in the invented PMU-assisted,
real-time static and dynamic ATC determination system: [0301] (1)
stator estimator and network topology analyzer from an energy
management system; [0302] (2) the invented real-time static and
dynamic power transfer capability system; [0303] (3) the real-time
measurement units such as PMUs, placed various locations including
a set of pre-determined interfaces; and [0304] (4) the real-time
ATC display system with both one-dimensional and two-dimensional
ATC monitoring system.
[0305] It should be pointed out that the solution methods of the
invented system can also determine the top-ranked interface static
and dynamic power transfer limit of each selected interface under
the contingency list associated with each interface.
[0306] This real-time dynamic ATC determination system has the
following features: [0307] (1) The real-time static and dynamic
security ATC calculation methodology determines the top-ranked
system-wide power transfer limits subject to both static and
dynamic security constraints of a contingency list. [0308] (2) The
system identifies, for each top-ranked power transfer limit, the
corresponding limiting contingency and the corresponding binding
constraint. [0309] (3) The system maps each top-ranked system-wide
power transfer limit into the power transfer limit of each selected
tie-line interface under the contingency. [0310] (4) The real-time
measurement of power flow across each selected tie-line interface
is obtained from the installed PMUs. For each limiting contingency,
the difference between the corresponding power transfer limit and
the current power transfer is the real-time available transfer
capability of the system associated with the top limiting
contingency and the corresponding binding constraint expressed as
the power flow across each interface.
[0311] Accordingly, it is to be understood that the embodiments of
the invention herein described are merely illustrative of the
application of the principles of the invention. Reference herein to
details of the illustrated embodiments is not intended to limit the
scope of the claims, which themselves recite those features
regarded as essential to the invention.
* * * * *